Modeling Symmetry, Asymmetry, and Change in Ordered Scales with Midpoints Using Adjacent Category Logit Models for Discrete Data

Likert scales and bipolar adjective scales are often used to measure attitudes and opinions. To model the dependence of the scale on covariates, investigators typically (1) assign interval scores to scale categories, using these in regression analyses; (2) collapse categories to compare responses above and below a middle category; or (3) estimate a model for the cumulative distribution, for example, a proportional odds model. Problems with Approaches 1 and 2 are obvious. However, Approach 3 is not easily used to address the concerns of researchers who work with these scales because cumulative probabilities are employed. Thus, this article constructs adjacent category logit models for analyzing such scales. The models, which incorporate discrete covariates, are linear in the logits, hence equivalent to log-linear models. The Appendix shows how to fit the models using standard software for estimating log-linear models. To illustrate, the author models the distribution of political views in the 1977 General Social Survey, by sex and education, as well as a 20-year series on sex role attitudes, using new models for trends.